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Simplifying 9x2 + 8x + 16 = 24x + 17 Reorder the terms: 16 + 8x + 9x2 = 24x + 17 Reorder the terms: 16 + 8x + 9x2 = 17 + 24x Solving 16 + 8x + 9x2 = 17 + 24x Solving for variable 'x'. Reorder the terms: 16 + -17 + 8x + -24x + 9x2 = 17 + 24x + -17 + -24x Combine like terms: 16 + -17 = -1 -1 + 8x + -24x + 9x2 = 17 + 24x + -17 + -24x Combine like terms: 8x + -24x = -16x -1 + -16x + 9x2 = 17 + 24x + -17 + -24x Reorder the terms: -1 + -16x + 9x2 = 17 + -17 + 24x + -24x Combine like terms: 17 + -17 = 0 -1 + -16x + 9x2 = 0 + 24x + -24x -1 + -16x + 9x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -1 + -16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -1.777777778x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -1.777777778x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -1.777777778x + x2 = 0 + 0.1111111111 -1.777777778x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -1.777777778x + x2 = 0.1111111111 The x term is -1.777777778x. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x + 0.7901234570 + x2 = 0.1111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 0.1111111111 + 0.7901234570 Combine like terms: 0.1111111111 + 0.7901234570 = 0.9012345681 0.7901234570 + -1.777777778x + x2 = 0.9012345681 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 0.9012345681 Calculate the square root of the right side: 0.94933375 Break this problem into two subproblems by setting (x + -0.888888889) equal to 0.94933375 and -0.94933375.Subproblem 1
x + -0.888888889 = 0.94933375 Simplifying x + -0.888888889 = 0.94933375 Reorder the terms: -0.888888889 + x = 0.94933375 Solving -0.888888889 + x = 0.94933375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 0.94933375 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 0.94933375 + 0.888888889 x = 0.94933375 + 0.888888889 Combine like terms: 0.94933375 + 0.888888889 = 1.838222639 x = 1.838222639 Simplifying x = 1.838222639Subproblem 2
x + -0.888888889 = -0.94933375 Simplifying x + -0.888888889 = -0.94933375 Reorder the terms: -0.888888889 + x = -0.94933375 Solving -0.888888889 + x = -0.94933375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -0.94933375 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -0.94933375 + 0.888888889 x = -0.94933375 + 0.888888889 Combine like terms: -0.94933375 + 0.888888889 = -0.060444861 x = -0.060444861 Simplifying x = -0.060444861Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.838222639, -0.060444861}
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